Many beneficial devices or structures in myriad applications are characterized at least in part by having a liquid that is in contact with at least one solid surface. For example, liquid droplets disposed on surfaces or within channels are the hallmarks of many microfluidic devices, biological/chemical sensors, chemical reactors, optical components, heat dissipation devices, and patterning applications. Many of these devices and applications are characterized in that liquid moves or is caused to be moved while in contact with a surface. Since the characteristics of both the liquid and the surface determine the interaction between the liquid and surface, it is often desirable to understand and control those characteristics to achieve control of the interaction of the liquid with those surfaces This is especially so when the application in question involves relatively small quantities of liquid.
FIG. 1 shows one illustrative prior art embodiment of small liquid droplet 102 disposed on a surface in a way such that it forms a liquid microlens 101. Such a liquid microlens is the subject of copending U.S. patent applications Ser. No. 09/884,605, filed Jun. 19, 2001, entitled “Tunable Liquid Microlens” and Ser. No. 09/951,637, filed Sep. 13, 2001, entitled “Tunable Liquid Microlens With Lubrication Assisted Electrowetting.” Both of these copending Patent Applications are hereby incorporated by reference herein in their entirety. The microlens embodiment of FIG. 1 is useful to demonstrate the interaction between any droplet of liquid and the surface on which it is disposed, whether or not the droplet and surface are part of a microlens or another application. In FIG. 1, droplet 102 is a droplet of a transparent liquid, such as water, typically (but not necessarily) with a diameter from several micrometers to several millimeters. The droplet is disposed on a transparent substrate 103 which is typically hydrophobic or includes a hydrophobic coating. The contact angle θ between the droplet and the substrate is determined by interfacial surface tensions (also known as interfacial energy) “γ”, generally measured in milli-Newtons per meter (mN/m). As used herein, γS-V is the interfacial tension between the substrate 103 and the air, gas or other liquid that surrounds the substrate, γL-V is the interfacial tension between the droplet 102 and the air, gas or other liquid that surrounds the droplet, and γS-L is the interfacial tension between the substrate 103 and the droplet 102. The contact angle θ may be determined from equation (1):cos θ=(γS-V−γS-L)/γL-V  Equation (1)
Equation (1) applies to any instance where a droplet of liquid is disposed on a surface, whether or not the droplet is used as a microlens.
In the microlens embodiment of FIG. 1 and in other instances where a liquid is disposed on a surface, it is often desirable to be able to change the shape of the droplet. FIG. 2 shows a prior art microlens 201, similar to the microlens of FIG. 1, whereby the phenomenon of electrowetting is used to change the shape of the droplet by reversibly changing the contact angle θ between droplet 202 of a conducting liquid and a dielectric insulating layer 203 having a thickness “d” and a dielectric constant ∈r. An electrode, such as metal electrode 204, is positioned below the dielectric layer 203 and is insulated from the droplet 202 by that layer. The droplet 202 may be, for example, a water droplet, and the dielectric insulating layer 203 may be, for example, a Teflon/Parylene surface.
When no voltage difference is present between the droplet 202 and the electrode 204, the droplet 202 maintains its shape defined by the volume of the droplet and contact angle θ1, where θ1 is determined by the interfacial tensions γ as explained above. When a voltage V is applied to the electrode 204, the voltage difference between the electrode 204 and the droplet 202 causes the droplet to spread. The dashed line 205 illustrates that the droplet 202 spreads equally across the layer 203 from its central position relative to the electrode 204. Specifically, the contact angle θ decreases from θ1 to θ2 when the voltage is applied between the electrode 204 and the droplet 202. By using separate electrodes under different parts of the droplet, and varying the voltage to those individual electrodes, spreading of the droplet can be achieved such that the droplet moves from its centered position to another desired position. Such a movement is described in the aforementioned copending '605 and '637 patent applications. The voltage V necessary to achieve this spreading, whether to change the shape of the droplet or its position, may range from several volts to several hundred volts. The amount of spreading, i.e., as determined by the difference between θ1 and θ2, is a function of the applied voltage V. The contact angle θ2 can be determined from equation (4):cos θ(V)=cos θ(V=0)+V2(∈0 ∈r)/(2dγL-V)  Equation (4)where cos θ (V=0) is the contact angle between the insulating layer 203 and the droplet 202 when no voltage is applied between the droplet 202 and electrode 204; γL-V is the droplet interfacial tension described above; ∈r is the dielectric constant of the insulating layer 203; and ∈0 is 8.85×10−12 F/M—the permittivity of a vacuum.
In implementations such as the liquid microlens described above, while the surface upon which the droplet is disposed is hydrophobic, the characteristics of that surface are such that the droplet flattens significantly at the area where it comes into contact with the surface. Thus, due to the resulting large contact area between the surface and the droplet, a significant amount of flow resistance is present between the surface and the droplet. This is desirable in the above microlens because, if there were too little flow resistance present, the droplet would freely move and it would become impossible to maintain the droplet in its desired stationary position or shape in the absence of other means for controlling the droplet. However, in many instances, it is often desirable to reduce the flow resistance experienced by a liquid on a surface.
Therefore, recent applications relying on liquids disposed on such surfaces have centered on attempts to reduce the aforementioned flow resistance exerted on the liquid. Many devices, such as those referred to above, can benefit from such a reduced flow resistance because of the resulting significant reduction in the operational power consumption of the devices. One such application is described in “Nanostructured Surfaces for Dramatic Reduction of Flow Resistance in Droplet-based Microfluidics”, J. Kim and C. J. Kim, IEEE Conf. MEMS, Las Vegas, Nev., January 2002, pp. 479-482, which is hereby incorporated by reference herein in its entirety. That reference generally describes how, by using surfaces with predetermined nanostructure features, the flow resistance to the liquid in contact with the surface can be greatly reduced.
The Kim reference teaches that, by finely patterning the surface in contact with the liquid, and using the aforementioned principle of liquid surface tension, it is possible to greatly reduce the area of contact between the surface and the liquid. It follows that the flow resistance to the liquid on the surface is correspondingly reduced.
FIGS. 3A-3F show how different, extremely fine-featured microstructure and nanostructure surface patterns result in different contact angles between the resulting surface and a droplet of liquid. FIGS. 3A and 3B show a microline surface and a micropost surface, respectively. Each of the lines 301 in FIG. 3A is approximately 3-5 micrometers in width and each of the microposts 302 in FIG. 3B is approximately 3-5 micrometers in diameter at its widest point. Comparing the microline pattern to the micropost pattern, for a given size droplet disposed on each of the surfaces, the contact area of the droplet with the microline pattern will be greater than the contact area of the droplet with the micropost pattern. FIGS. 3D and 3E show the contact angle of a droplet relative to the microline surface of FIG. 3A and the micropost surface of FIG. 3B, respectively. The contact angle 303 of the droplet 305 on the microline pattern is smaller (˜145 degrees) than the contact angle 304 of the droplet 306 with the micropost pattern (˜160 degrees). As described above, it directly follows that the flow resistance exerted on the droplet by the microline pattern will be higher than that exerted by the micropost pattern.
FIG. 3C shows an even finer pattern than that of the microline and micropost pattern. Specifically, FIG. 3C shows a nanopost pattern with each nanopost 309 having a diameter of less than 1 micrometer. While FIG. 3C shows nanoposts 309 formed in a somewhat conical shape, other shapes and sizes are also achievable. In fact, cylindrical nanopost arrays have been produced with each nanopost having a diameter of less than 10 nm. Specifically, FIGS. 4A-4E show different illustrative arrangements of nanoposts produced using various methods and further show that such various diameter nanoposts can be fashioned with different degrees of regularity. Moreover, these figures show that it is possible to produce nanoposts having various diameters separated by various distances. An illustrative method of producing nanoposts, found in U.S. Pat. No. 6,185,961, titled “Nanopost arrays and process for making same,” issued Feb. 13, 2001 to Tonucci, et al, is hereby incorporated by reference herein in its entirety. Nanoposts have been manufactured by various methods, such as by using a template to form the posts, by various means of lithography, and by various methods of etching.
Referring to FIG. 3F, a droplet 307 disposed on the nanopost surface of FIG. 3C, is nearly spherical with a contact angle 308 between the surface and the droplet equal to between 175 degrees and 180 degrees. The droplet 307 disposed on this surface experiences nearly zero flow resistance. As a result, as is noted by the Kim reference, prior attempts at placing a droplet on such a surface were problematic, as this extremely low flow resistance made it almost impossible to keep the water droplets stationary on the nanostructured surface. As shown in FIG. 5, the reason for this low flow resistance is that the surface tension of droplet 501 of an appropriate liquid (depending upon the surface structure) will enable the droplet 501 to be suspended on the tops of the nanoposts with no contact between the droplet and the underlying solid surface. This results in an extremely low area of contact between the droplet and the surface (i.e., the droplet only is in contact with the top of each post 502) and, hence low flow resistance.
Thus, as exemplarily taught by the Kim reference, prior attempts to reduce flow resistance of liquids through the use of nanostructures have been limited to disposing the droplets in a narrow channel, tube or other enclosure to control the freedom movement of the droplet to within a prescribed area.